A250523 Number of (n+1)X(4+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.

3123, 18859, 82023, 300131, 993123, 3088923, 9240559, 26984403, 77707851, 222271083, 634724183, 1815888579, 5216209523, 15062616251, 43743061503, 127741126963, 374944674139, 1105460634123, 3271582279911, 9712201092643

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).

Empirical g.f.: x*(3123 - 24863*x + 83452*x^2 - 163338*x^3 + 214295*x^4 - 196963*x^5 + 119218*x^6 - 39828*x^7 + 5832*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - Colin Barker, Nov 14 2018

Example

Some solutions for n=3:
..2..2..1..1..0....0..1..1..0..0....2..0..0..0..0....2..1..2..1..1
..1..1..1..1..0....1..2..2..2..2....1..0..0..1..2....1..0..1..0..0
..0..0..1..2..1....0..1..1..1..1....1..0..0..1..2....0..0..1..0..0
..0..0..1..2..1....0..1..2..2..2....1..0..0..1..2....0..0..1..0..2

Crossrefs

Column 4 of A250527.

Sequence in context: A107535 A181285 A133526 * A251061 A213193 A102709

Adjacent sequences: A250520 A250521 A250522 * A250524 A250525 A250526

Keyword

nonn

Author

R. H. Hardin, Nov 24 2014

Status

approved